Determine whether the function below is exponential decay, and find the percentage rate of change.
P(t)=3.5(0.91)^t
A exponential growth; 3.5%
B exponential decay; 3.5%
C exponential decay; 9%
D exponential growth; 9%
The function P(t)=3.5(0.91)^t is exponential decay because the base of the exponential function, 0.91, is between 0 and 1. To find the percentage rate of change, we need to determine the percentage decrease per unit change in t.
The base of the exponent, 0.91, represents a decrease of 100% - 91% = 9%. Therefore, the percentage rate of change is 9%.
So the correct answer is:
C exponential decay; 9%